The present invention relates to nuclear magnetic resonance (NMR) logging, and more particularly to a method and system for processing different signals in the time domain to obtain a composite signal that is optimized in terms of its transform domain resolution.
Nuclear magnetic resonance (NMR) logging has become an important input to formation evaluation in hydrocarbon exploration and is one of the preferred methods for determining formation parameters. Improvements in hardware as well as advances in data analysis and interpretation allow log analysts to generate detailed reservoir description reports, including clay-bound and capillary-bound related porosity, estimates of the amounts of bound and free fluids, fluid types (i.e., oil, gas and water), as well as permeability, based on NMR logs.
The basic input for analysis of NMR data are spectra of the transversal NMR relaxation time T2 calculated from pulse-echo trains. Several issues arise in this context, and are considered in some detail next.
T2 resolution
T2 resolution is affected by several parameters of the echo train, including the inter-echo spacing, echo train length and the noise.
Generally, the temporal length of the echo trains determines the maximum T2 that can be resolved. FIG. 1 shows the normalized error between an input model and a T2 inversion result as a function of echo train length, and in particular indicates the longest resolvable T2 component as a function of the echo train length. The solid line shows the exact modeling results, while the dashed line represents the trend. The results were modeled using a Monte Carlo method, the noise standard deviation was "sgr"=1 p.u. FIG. 1 suggests that the longest resolvable T2 component is on the order of 2-3 times the length of the echo train. This is indicated in the figure by a sharp increase of the normalized error for T2/echo-train-length ratio greater than 2. Theoretically, Whittall et al. (see the reference below) have found that the xe2x80x9cresolving powerxe2x80x9d of the echo train is proportional to
SNRxe2x80xa2{square root over (Ne)}xe2x80x83xe2x80x83(1) 
where SNR is the signal-to-noise ratio of the signal and Ne is the number of echoes. FIG. 1 in combination with Eq. (1) indicates that the echo train length (Texe2x80xa2Ne) has a stronger influence on the longest T2 that can be resolved than the noise.
Further modeling results support the assumption that noise is critical for the resolution of fast T2 components. FIG. 2 shows the normalized error between fast T2 components (0.5 to 3 ms) and the input model as a function of noise. The inter-echo spacing Te is 0.6 ms, "sgr" ranges from 0.1 to 10 p.u. As expected, the uncertainty in determining fast T2 components increases with the amount of noise.
Another aspect to consider is the ability to resolve fast T2 components with respect to inter-echo spacing Te. The modeling results are presented in FIG. 3. The noise standard deviation is "sgr"=1 p.u. The normalized error is shown as a function of the fastest T2 component normalized by Te. The fastest T2 component, which can be resolved, is on the order of the inter-echo-spacing Te. Note that this holds true only if the first echo (recorded after one Te-time) is included in the inversion. The results presented above allow the following conclusions:
(1) The resolution of fast T2 components depends both on Te and noise. Low noise on the early echoes is as important as a small Te to obtain accurate short T2""s; and
(2) The temporal echo train length is the limiting factor for the resolution of long T2 relaxation times. Noise does not play such an important role.
Note that all results were calculated using the fast T2 inversion technique introduced by Prammer (MAP ALGORITHM (see reference to paper SPE 28368 below). It is expected that other inversion techniques will produce similar results.
Noise Optimization
Edwards and Chen suggested to improve the accuracy of results from NMR well logs by time-dependent filtering of echo train data. (see reference to paper RR below). They recommend applying a relatively weak filter on early echoes and gradually increasing the filter strength for later echoes. The results outlined above indicate that no significant improvement in T2 resolution will be achieved by filtering.
Other methods, such as xe2x80x9cwindowing techniquesxe2x80x9d suffer from similar limitations. In order to preserve the information contents of the early echoes (yielding fast T2 components), the window length for the early echoes has to be very short. Since a window length of 2 would effectively double the minimal T2 component, a common practice is to set the window length to 1 for the first echoes, i.e., use the early echoes instead of windows. This highlights the importance of recording good, low noise, early echoes in the first place. With a multi-volume tool this can be done efficiently by stacking, while single volume tools need to sacrifice logging speed.
Prammer et al. introduced a technique, originally designed for a dual-volume NMR logging tool, to record low noise pulse-echo data. (See reference to Prammer et al., paper SPE 36522 below). The method allows to acquire pulse-echo NMR data covering the entire geologically meaningful T2 range (approximately between 0.5 ms and 2 sec.) with adequate resolution and precision at acceptable logging speeds.
Essentially, two sets of data are recorded (quasi) simultaneously. One data stream consists of short stacked, low noise, echo trains with Te=0.6 ms. The second data set includes long echo trains. It is recognized in the art that the early echoes of a CPMG pulse-echo data are significant for the determination of fast T2 components. Slow T2 components on the other hand can only be resolved with long echo trains.
The method involves recording blocks of short, under-polarized echo trains resolving the fast relaxation components T2, interleaved with long, fully polarized echo trains that allow the determination of slow components. The two echo trains are analyzed separately and the partial spectra are combined to obtain a complete spectrum. This technique, developed for NUMAR Corporation""s (a Halliburton Company) dual-volume tool (MRIL(copyright) C/TP*), allows acceptable logging speeds, while acquiring NMR logs of good quality. For a more detailed discussion of the method, the reader is directed to application Ser. No. 08/816,395 filed Mar. 13, 1997 to one of the co-inventors of this application, which is hereby incorporated by reference for all purposes. Extending the effective range of T2 measurements using multiple quasi-simultaneous measurements represents an important advancement of the art.
It should be noted that while the wait time Tw between two long data sets is sufficiently long to fully polarize the hydrogen atoms, the 0.6 ms data used in the Prammer et al. method is recorded with a wait time of about Tw=20 ms. Thus the long components in the 0.6 ms data are not fully polarized. Hence the two data sets are inverted into T2 domain separately. (See reference to paper SPE 36522 below).
In a separate step the two partial spectra are combined into one spectrum covering the full T2 range. Although this method provides good results in most cases, the choice of the xe2x80x9ccombining pointxe2x80x9d of the two input spectra introduces some uncertainty. (See the references to Chen et al., paper SCA 9702; and Dunn et al., paper JJ cited below).
Another set of issues is presented by the latest generation of NMR logging tools (MRIL(copyright) Series D to NUMAR Corporation, a Halliburton company) that extend the concept of combining different echo trains and provide further analysis flexibility. These multi-volume instruments allow to simultaneously record NMR data with different inter-echo spacing Te, wait time Tw, and signal-to-noise ratio (SNR). Each part of the data set can emphasize different NMR properties. That way, almost universal data can be acquired in single-pass operation. The problem then remains how to combine data sets in efficient and statistically meaningful ways that enhance the performance of the logging tools.
One approach is suggested in the Prammer et al. method considered above, where to obtain the complete T2 spectra, different kinds of echo trains (i.e., short high-precision echo trains recorded with a short wait time Tw, and long echo trains with long Tw) are inverted in two sets of T2. The first set covers fast T2, while the second set resolves medium and long T2. In a subsequent step the two partial spectra are concatenated. Notably the combination of different T2 information is carried out in the T2 domain.
Several authors (see the Chen and Georgi, paper SCA 9702; Dunn et al., paper JJ; references cited below) pointed out shortcomings of this method: (a) The xe2x80x9cconcatenation pointxe2x80x9d of the T2 spectra is a source of uncertainty; (b) Straight T2 spectra concatenation, i.e., without interpolation or tapering, can introduce artifacts into the final result; (c) T2 spectra concatenation does not take into account any SNR difference between the two input spectra; (d) Other information embedded in the echo trains such as the longitudinal NMR relaxation time T1 is ignored.
Chen and Georgi tried to minimize some of the uncertainty of T2 spectra concatenation by calculating the clay bound water related porosity (CBW) from a partially recovered echo train. A back-transformed echo train representing the CBW porosity is then subtracted from a fully recovered echo train. They invert the correct echo train and merge the spectra (from partial recovered and fully recovered data) in the T2 domain. This approach is limited in that: (a) The method is based on the assumption that all clay bound water is polarized in the partial recovered data. While this is true for most situations, examples have been found where this is not the case; (b) The xe2x80x9cconcatenation pointxe2x80x9d of the T2 spectra is still a source of uncertainty; (c) The method does not take into account any SNR difference between the two input data sets.
Dunn et al. (see the list of references below) suggested a method to simultaneously invert two echo trains recorded with different Tw into the T2 domain. The proposed Composite-Data-Processing (CDP) method solves a linear equation system simultaneously for the two different echo trains in a least square sense. The CDP method has other limitations, including: (a) It requires a priori information about T1; (b) In their implementation of CDP, Dunn et al. assume a constant T1, which is not necessarily the case; (c) The difference in SNR between the two input echo trains is not exploited. Notably, the CDP does not merge echo trains. The combination of different T2 information is rather done in an xe2x80x9cequation domainxe2x80x9d.
Further background information on these issues can be found in the following references, the content of which is hereby incorporated by reference for all purposes.
1. Prammer, M. G., Drack, E. D., Bouton, J. C., Gardner, J. S., Coates, G. R., Chandler, R. N., Miller, M. N.: xe2x80x9cMeasurements of Clay-Bound Water and Total Porosity by Magnetic Resonance Loggingxe2x80x9d, paper SPE 36522 presented at the 71st Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Denver, Oct. 6-9, 1996.
2. Prammer, M. G.: xe2x80x9cNMR Pore Size Distribution and Permeability at the Well Sitexe2x80x9d, paper SPE 28368 presented at the 69th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, Sept. 25-28, 1994.
3. Chen, S., Georgi, D. T.: xe2x80x9cImproving the Accuracy of NMR Relaxation Distribution Analysis in Clay-Rich Reservoirs and Core Samplesxe2x80x9d, paper SCA 9702, in 1997 international symposium proceedings: Society of Professional Well Log Analysts, Society of Core Analysts Chapter-at-large, p. 10, 1997.
4. Dunn, K-J., Bergman, D. J., LaTorraca, G. A., Stonard, S. M., Crowe, M. B.: xe2x80x9cA Method for Inverting NMR Data Sets with Different Signal To Noise Ratiosxe2x80x9d, paper JJ presented at the 39th Annual Logging Symposium of the Society of Professional Well Log Analysts, Keystone, May 26-29, 1998.
5. Menger, S., Pranmner, M.: xe2x80x9cA New Algorithm for Analysis of NMR Logging Dataxe2x80x9d, paper SPE 49013 accepted for the 73rd Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, Sep. 27-30, 1998.
6. Coates, G. R., Menger, S., Prammer, M., Miller, D.: xe2x80x98Applying NMR Total and Effective Porosity to Formation Evaluationxe2x80x99, paper SPE 38736 presented at the 72nd Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, San Antonio, Oct. 5-8, 1997.
7. Chandler, R. N., Drack, E. D., Miller, M. N., Prammer, M. G.:xe2x80x9cImproved Log Quality with Dual-Frequency Pulsed NMR Toolxe2x80x9d, paper SPE 28365 presented at the 69th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, Sept. 25-28, 1994.
8. Whittal, K. P., Bronskill, M., Henjelman, R. M.: xe2x80x98Investigation of Analysis Techniques for Complicated NMR Relaxation Dataxe2x80x99, J. Magn. Reson., 95, 221, 1991.
9. Edwards, C. E., Chen, S.: xe2x80x98Improved NMR Well Logs from Time-Dependent Echo Filteringxe2x80x99, paper RR presented at the 37th Annual Logging Symposium of the Society of Professional Well Log Analysts, New Orleans, Jun. 16-19, 1996.
Additionally, collecting NMR data, constructing uni-exponential and multi-exponential models, and other NMR signal processing is known in the art and is described, for example, in U.S. Pat. Nos. 5,212,447; 5,280,243; 5,309,098; 5,412,320; 5,517,115; 5,557,200, and 5,696,448 to the assignee of the present application, as well as, application Ser. No. 08/816,395 filed Mar. 13, 1997 to one of the co-inventors of this application, which are hereby incorporated by reference for all purposes.
In view of the shortcomings of the prior art briefly summarized above, it is apparent that there is a need for a method and system that can take full advantage of the flexibility provided by current-generation NMR tools and enable the calculation of high-resolution T2 spectra of the input signal over the entire geologically meaningful range of values. It is thus an object of the present invention to provide such a method and system that obviate problems associated with the prior art.
In particular, in accordance with the present invention a new method is proposed that allows to merge echo trains acquired with different parameters, comprising inter-echo spacing, wait time, and signal-to-noise ratio into one single echo train. In accordance with this invention, the merging is carried out in the time-domain. Amplitude correction is applied to adjust the value of partially recovered echo trains to fully recovered trains. A priori information about T1, if available, can be used to make this adjustment directly. However, a priori information about T1 is not required, because it may be extracted using the method of this invention. The merged echo train obtained in accordance with the present invention is optimized with respect to T2 resolution. As a result of the application of the novel method, the complete T2 spectrum can be calculated in a single step, with good resolution over its entire range of values.
To overcome limitations of the prior art methods used to compute complete T2 spectra, in accordance with the present invention it is proposed to merge echo trains in the time domain, i.e., to merge different echo trains. In a preferred embodiment, the input echo trains can be acquired with different Te, Tw, and SNR using, for example, NUMAR""s MRIL(copyright) tool, D series. By combining two or more echo trains with different Te and signal-to-noise ratios, a single resulting echo train can be obtained, which is optimized in terms of T2 resolution. This echo train serves as input for T2 inversion algorithms, that can handle echo trains with different Te and SNR, such as the MAP algorithm (see Prammer et al., paper SPE 28368). In accordance with a preferred embodiment, if the input echo trains are acquired with Tw too short to allow the protons to filly polarize (i.e., with partial recovery), the respective amplitude is adjusted to match the fully recovered echo data. The amount of amplitude adjustment provides information about the T1 relaxation time.
More specifically, in accordance with the present invention, a method for conducting NMR logging measurements is disclosed, comprising: (a) providing at least one first echo train acquired using a first set of echo train parameters, said first echo train carrying information about relatively fast-relaxation NMR signals; (b) providing at least a second echo train acquired using a second set of echo train parameters, said second echo train carrying information about relatively slow-relaxation NMR signals; and (c) merging said at least one first and said at least one second echo trains in the time domain to obtain a merged echo train carrying information about both relatively fast and relatively slow NMR signals. In a specific embodiment, the first echo train(s) correspond to partially recovered NMR signals, and the second echo train(s) correspond to fully recovered NMR signals. In this embodiment, the method further comprises adjusting the amplitude of said partially recovered NMR signals to the amplitude of said relatively slow-relaxation NMR signals, where the adjustment can be performed in the time domain, and may take into account information about the T1 spectrum of the signal.
In another aspect, the invention is a method for conducting NMR logging measurements with enhanced transform domain resolution, comprising: providing two or more NMR echo trains, each of said echo trains having parameters selected to cover a portion of the T2 spectrum; combining said two or more NMR echo trains in the time domain into a merged echo train; and inverting the merged echo train to the T2 spectrum domain to obtain information about the properties of an underlying material. In a specific embodiment, at least one of the two or more NMR echo trains corresponds to partially recovered NMR signals and at least one of the two or more NMR echo trains corresponds to fully recovered NMR signals, in which case the amplitude of the partially recovered NMR signals are preferably adjusted to the amplitude of the fully recovered NMR signals. In an important aspect of the invention, at least two of the two or more NMR echo trains are acquired quasi-simultaneously. In another important aspect, at least two of the two or more NMR echo trains are acquired in different sensitive volumes.
In another aspect, the invention is a method of operating a multi-volume NMR logging tool, comprising: (a) acquiring a first NMR echo train or sets of echo trains in a first sensitive volume of the tool, said first echo train(s) carrying information about relatively fast-relaxation NMR signals; (b) acquiring a second NMR echo train or sets of echo trains in a second sensitive volume of the tool, said second echo train(s) carrying information about relatively slow-relaxation NMR signals; and (c) merging said first and said second echo train(s) in the time domain to obtain a merged echo train carrying information about both relatively fast-relaxation and relatively slow-relaxation NMR signals. In a specific preferred embodiment, the first echo train(s) and said second echo train(s) are acquired quasi-simultaneously.